If the resistance in the coil is 2.0 , what is the magnitude of the induced current in the coil while the field is changing

This question is incomplete, the complete question is;

A coil consists of 200 turns of wire. Each turn is a square of side 18 cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.80 s,

a) what is the magnitude of the induced emf in the coil while the field is changing?

b) if the resistance of the coil is 2.0, what is the magnitude of the induced current in the coil while the field is changing?

Answer:

a) the magnitude of the induced emf in the coil is 4.05 V

b) induced current in the coil I is 2.025 A

Explanation:

Given that;

side of turn a = 18 cm = 0.18 m

no. of turns N = 200

dB = 0.50 T

time t = 0.80 sec

(a)

what is the magnitude of the induced emf in the coil while the field is changing?

we know that the magnetic flux is equal to the product of the magnetic field in a loop and the area of the loop so;

 ∅ = NBA

expression for the electromotive force is expressed as;

∈ = d∅/dt

Now replace NBA for ∅ in the above equation.

∈ = d(NBA) / dt

= NA(dB/dt)

The expression for the area of each square turn is expressed as follows

A = a²

a is the side of the turn

so we substitute the value of a

A = (0.18) ²

A= 0.0324 m²

 As  earlier derived

formula for the electromotive force is as follows:

∈  = NA(dB/dt)

so we substitute all our values

∈ =  (200)(0.0324m²) (0.50T/0.80s)

∈ = 6.48 × 0.625

∈ = 4.05 V

Therefore the magnitude of the induced emf in the coil is 4.05 V

(b)

if the resistance of the coil is 2.0, what is the magnitude of the induced current in the coil while the field is changing?

we know that the current induced in the circuit is equal to the ratio between the electromotive forces to the resistance of the ring so;

I = ∈ / R

given that; resistance of the coil = 2.0

so we substitute

I = 4.05 / 2.0

I = 2.025 A

Therefore induced current in the coil I is 2.025 A

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